Locating an element by id

Your question is very difficult to answer, certainly to give a single conclusive answer. In fact, I am tempted to flag this question as "too broad", which is supported by the other answers and comments.

Take, for example, just your element(by.id("id"));. Looking through the Selenium source, most drivers just take whatever id you give, and pass it off to the wire protocol:

public WebElement findElementById(String using) {
  if (getW3CStandardComplianceLevel() == 0) {
    return findElement("id", using);
  } else {
    return findElementByCssSelector("#" + cssEscape(using));
  }
}

As you know, each browser vendor implements their own wire protocol in a separate binary. Feel free to go further into the code, to dig a deeper hole for your self.

For other browsers that do not support the wire protocol, for example HtmlUnit, you just have something like:

public List<WebElement> findElementsById(String id) {
  return findElementsByXPath("//*[@id='" + id + "']");
}

and then they parse the available DOM.

As for your performance question, anything that anyone gives you will be 1) just a feeling, or 2) pure BS! Which you can already see from the other answers and comments you are getting.

To get a real answer (supported by actual data), there are just too many variables to consider:

Wire protocol as implemented by different browser vendors, plus various optimizations in different versions.
DOM engines as implemented by different browser vendors, plus various optimizations in different versions.
JavaScript engines as implemented by different browser vendors, plus various optimizations in different versions.

Also, whatever results you get for your web app / web page will most like not apply to a different web app / web page, due to differences in the framework used to build that site.

Bottom line is: If you are concerned about performance testing, then Selenium is the wrong answer. Selenium is a functional test library, optimized to give you the best end-user representation. Performance is a distant afterthought.

If your goal is to get your tests to run faster, your time will be better spent looking at your test structure:

How frequently do you open/close the browser. This is often the most time consuming activity in a test.
How often do you refresh your element cache, how often do you need to? Consider moving your elements to Page Factory model, which lazy-loads all elements for you.
And of course the biggest speedup factor: running your tests in parallel on multiple machines.

But I think this is getting off topic (some might suggest "ranty") from your initial question.

I just think about performance perspective and write the following script to check google logo. Although the result is confusing, we can make an estimation the result statistically.

querySelector and getElementById have always better result, unless number of trials is more than 10K. If we compare these two method: getElementById is better (29 over 21).

If we compare these there, ID, CSS and XPATH, CSS is better (29 over 18 and 4), second is ID and last one XPATH.

The result from my test: getElementById, querySelector, CSS, ID, XPATH

See the table, result and script:

Table show the result in summary for 50 tries:

                1   2   3   4   5
ID              0   0   18  24  8
CSS             0   0   29  18  3
XPATH           0   0   4   12  34
querySelector   21  29  0   0   0
getElementById  29  21  0   0   0

Result with time diff:

>>> for i in range(50):
...  test_time(1)
...
[('getElementById', 0.004777193069458008), ('querySelector', 0.006440162658691406), ('id', 0.015267133712768555), ('css', 0.015399932861328125), ('xpath', 0.015429019927978516)]
[('querySelector', 0.006442070007324219), ('getElementById', 0.00728607177734375), ('id', 0.013181924819946289), ('css', 0.014509916305541992), ('xpath', 0.015583992004394531)]
[('getElementById', 0.0063440799713134766), ('querySelector', 0.006493091583251953), ('css', 0.014523029327392578), ('id', 0.014902830123901367), ('xpath', 0.015790224075317383)]
[('getElementById', 0.007112026214599609), ('querySelector', 0.007357120513916016), ('id', 0.014781951904296875), ('css', 0.015780925750732422), ('xpath', 0.016005992889404297)]
[('getElementById', 0.006434917449951172), ('querySelector', 0.007117033004760742), ('id', 0.01497507095336914), ('css', 0.015005111694335938), ('xpath', 0.015393972396850586)]
[('querySelector', 0.00563812255859375), ('getElementById', 0.006503105163574219), ('css', 0.014302968978881836), ('id', 0.014812946319580078), ('xpath', 0.017061948776245117)]
[('querySelector', 0.0048770904541015625), ('getElementById', 0.006540060043334961), ('css', 0.014795064926147461), ('id', 0.015192985534667969), ('xpath', 0.016000986099243164)]
[('getElementById', 0.006265878677368164), ('querySelector', 0.006501913070678711), ('id', 0.014132022857666016), ('css', 0.01437997817993164), ('xpath', 0.014840841293334961)]
[('getElementById', 0.006368160247802734), ('querySelector', 0.006601095199584961), ('css', 0.01462101936340332), ('id', 0.014872074127197266), ('xpath', 0.016145944595336914)]
[('querySelector', 0.00642704963684082), ('getElementById', 0.006908893585205078), ('css', 0.014439105987548828), ('id', 0.014970064163208008), ('xpath', 0.015510082244873047)]
[('getElementById', 0.006404876708984375), ('querySelector', 0.006679058074951172), ('css', 0.014878988265991211), ('id', 0.01546788215637207), ('xpath', 0.015535116195678711)]
[('querySelector', 0.005848884582519531), ('getElementById', 0.008013010025024414), ('css', 0.014436006546020508), ('xpath', 0.01566910743713379), ('id', 0.015830039978027344)]
[('querySelector', 0.006299018859863281), ('getElementById', 0.006538867950439453), ('css', 0.014534950256347656), ('id', 0.014979124069213867), ('xpath', 0.01618194580078125)]
[('getElementById', 0.006415128707885742), ('querySelector', 0.006479978561401367), ('id', 0.014901876449584961), ('css', 0.014998912811279297), ('xpath', 0.01544499397277832)]
[('getElementById', 0.006515979766845703), ('querySelector', 0.006515979766845703), ('xpath', 0.014292001724243164), ('css', 0.014482975006103516), ('id', 0.015102863311767578)]
[('getElementById', 0.00574803352355957), ('querySelector', 0.006389141082763672), ('css', 0.014650821685791016), ('id', 0.014751911163330078), ('xpath', 0.01532888412475586)]
[('getElementById', 0.0063037872314453125), ('querySelector', 0.006974935531616211), ('id', 0.014775991439819336), ('css', 0.014935970306396484), ('xpath', 0.015460968017578125)]
[('getElementById', 0.0064661502838134766), ('querySelector', 0.0065021514892578125), ('id', 0.014723062515258789), ('css', 0.014946937561035156), ('xpath', 0.015508890151977539)]
[('getElementById', 0.006738901138305664), ('querySelector', 0.008143901824951172), ('css', 0.014575004577636719), ('xpath', 0.015228986740112305), ('id', 0.015702009201049805)]
[('getElementById', 0.006436824798583984), ('querySelector', 0.0064470767974853516), ('css', 0.014545917510986328), ('id', 0.014694929122924805), ('xpath', 0.015357017517089844)]
[('querySelector', 0.006292104721069336), ('getElementById', 0.006451845169067383), ('css', 0.014657020568847656), ('xpath', 0.01574397087097168), ('id', 0.016795873641967773)]
[('getElementById', 0.006443977355957031), ('querySelector', 0.006485939025878906), ('css', 0.013139009475708008), ('id', 0.014308929443359375), ('xpath', 0.015516042709350586)]
[('querySelector', 0.006464958190917969), ('getElementById', 0.006821870803833008), ('id', 0.016110897064208984), ('css', 0.01633286476135254), ('xpath', 0.017225980758666992)]
[('getElementById', 0.005715131759643555), ('querySelector', 0.008069992065429688), ('css', 0.014779090881347656), ('id', 0.01491093635559082), ('xpath', 0.015527963638305664)]
[('getElementById', 0.006309986114501953), ('querySelector', 0.006836891174316406), ('css', 0.01497507095336914), ('id', 0.015040159225463867), ('xpath', 0.02096104621887207)]
[('querySelector', 0.00616908073425293), ('getElementById', 0.007357120513916016), ('css', 0.014974832534790039), ('id', 0.015640974044799805), ('xpath', 0.016278982162475586)]
[('querySelector', 0.005301952362060547), ('getElementById', 0.0063440799713134766), ('id', 0.014526844024658203), ('css', 0.014657974243164062), ('xpath', 0.0162200927734375)]
[('querySelector', 0.005811929702758789), ('getElementById', 0.007221221923828125), ('css', 0.01259613037109375), ('xpath', 0.014851093292236328), ('id', 0.015043020248413086)]
[('getElementById', 0.006195068359375), ('querySelector', 0.007548093795776367), ('css', 0.01441502571105957), ('id', 0.01441812515258789), ('xpath', 0.016713857650756836)]
[('querySelector', 0.0050449371337890625), ('getElementById', 0.006323099136352539), ('id', 0.01497793197631836), ('css', 0.014984130859375), ('xpath', 0.015444040298461914)]
[('getElementById', 0.007039070129394531), ('querySelector', 0.008107900619506836), ('xpath', 0.015566825866699219), ('id', 0.015954017639160156), ('css', 0.01815509796142578)]
[('getElementById', 0.005831003189086914), ('querySelector', 0.007988214492797852), ('id', 0.014652013778686523), ('css', 0.014683008193969727), ('xpath', 0.01581597328186035)]
[('querySelector', 0.006363868713378906), ('getElementById', 0.006494998931884766), ('xpath', 0.01517796516418457), ('id', 0.016071796417236328), ('css', 0.017260074615478516)]
[('getElementById', 0.00633692741394043), ('querySelector', 0.007826089859008789), ('css', 0.014354944229125977), ('id', 0.015484809875488281), ('xpath', 0.017076969146728516)]
[('querySelector', 0.006349802017211914), ('getElementById', 0.006428956985473633), ('css', 0.01385188102722168), ('id', 0.014858007431030273), ('xpath', 0.016836166381835938)]
[('querySelector', 0.006417989730834961), ('getElementById', 0.007012844085693359), ('css', 0.01460719108581543), ('id', 0.014763832092285156), ('xpath', 0.015476226806640625)]
[('getElementById', 0.006266117095947266), ('querySelector', 0.0074520111083984375), ('id', 0.014987945556640625), ('css', 0.01515817642211914), ('xpath', 0.015646934509277344)]
[('getElementById', 0.006376981735229492), ('querySelector', 0.0064089298248291016), ('id', 0.01494598388671875), ('css', 0.015275001525878906), ('xpath', 0.01553201675415039)]
[('getElementById', 0.006357908248901367), ('querySelector', 0.006699085235595703), ('css', 0.014505147933959961), ('xpath', 0.015446186065673828), ('id', 0.019747018814086914)]
[('getElementById', 0.0063610076904296875), ('querySelector', 0.0064640045166015625), ('css', 0.014472007751464844), ('id', 0.014828205108642578), ('xpath', 0.01532888412475586)]
[('getElementById', 0.0063610076904296875), ('querySelector', 0.006580829620361328), ('css', 0.012439966201782227), ('id', 0.014935016632080078), ('xpath', 0.015373945236206055)]
[('querySelector', 0.006309032440185547), ('getElementById', 0.006561994552612305), ('id', 0.014923095703125), ('css', 0.015380859375), ('xpath', 0.01574110984802246)]
[('querySelector', 0.006357908248901367), ('getElementById', 0.006387948989868164), ('css', 0.01481485366821289), ('id', 0.015089988708496094), ('xpath', 0.015390872955322266)]
[('querySelector', 0.004536867141723633), ('getElementById', 0.00640416145324707), ('css', 0.014551877975463867), ('xpath', 0.014974117279052734), ('id', 0.014991998672485352)]
[('getElementById', 0.006387233734130859), ('querySelector', 0.00643610954284668), ('css', 0.014494895935058594), ('id', 0.014873981475830078), ('xpath', 0.015212059020996094)]
[('getElementById', 0.0063588619232177734), ('querySelector', 0.006443977355957031), ('css', 0.013200998306274414), ('id', 0.014631986618041992), ('xpath', 0.015624046325683594)]
[('getElementById', 0.0048558712005615234), ('querySelector', 0.005300045013427734), ('id', 0.014750003814697266), ('css', 0.014846086502075195), ('xpath', 0.015408992767333984)]
[('querySelector', 0.008347034454345703), ('getElementById', 0.008370161056518555), ('id', 0.014650106430053711), ('css', 0.014775991439819336), ('xpath', 0.015323877334594727)]
[('querySelector', 0.006309032440185547), ('getElementById', 0.007323026657104492), ('css', 0.014546871185302734), ('xpath', 0.015864133834838867), ('id', 0.02078390121459961)]
[('querySelector', 0.007790088653564453), ('getElementById', 0.010209083557128906), ('id', 0.015320062637329102), ('xpath', 0.01600193977355957), ('css', 0.01807403564453125)]

Code:

from timeit import default_timer as timer
import time, operator
from selenium import webdriver

def open_browser():
    dr = webdriver.Chrome()
    dr.get('http://www.google.com')
    time.sleep(5)
    return dr,timer()

def quit_browser(el, start, dr, result):
    diff = timer() - float(start)
    result[el] = diff
    dr.quit()

def test_time(tm):
    result = {}
    
    dr, start = open_browser()
    for i in range(tm):
        dr.find_element_by_id('hplogo')
    quit_browser("id", start, dr, result)
    
    dr, start = open_browser()
    for i in range(tm):
        dr.find_element_by_css_selector('#hplogo')
    quit_browser("css", start, dr, result)
    
    dr, start = open_browser()
    for i in range(tm):
        dr.find_element_by_xpath("//*[@id='hplogo']")
    quit_browser("xpath", start, dr, result)
    
    dr, start = open_browser()
    for i in range(tm):
        dr.execute_script("return document.querySelector('#hplogo');")
    quit_browser("querySelector", start, dr, result)
    
    dr, start = open_browser()
    for i in range(tm):
        dr.execute_script("return document.getElementById('hplogo');")
    quit_browser("getElementById", start, dr, result)
    
    print sorted(result.items(), key=operator.itemgetter(1))

Locating an element by id

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